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Mirrors > Home > ILE Home > Th. List > ralrnmpo | Unicode version |
Description: A restricted quantifier over an image set. (Contributed by Mario Carneiro, 1-Sep-2015.) |
Ref | Expression |
---|---|
rngop.1 | |
ralrnmpo.2 |
Ref | Expression |
---|---|
ralrnmpo |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rngop.1 | . . . . 5 | |
2 | 1 | rnmpo 5932 | . . . 4 |
3 | 2 | raleqi 2656 | . . 3 |
4 | eqeq1 2164 | . . . . 5 | |
5 | 4 | 2rexbidv 2482 | . . . 4 |
6 | 5 | ralab 2872 | . . 3 |
7 | ralcom4 2734 | . . . 4 | |
8 | r19.23v 2566 | . . . . 5 | |
9 | 8 | albii 1450 | . . . 4 |
10 | 7, 9 | bitr2i 184 | . . 3 |
11 | 3, 6, 10 | 3bitri 205 | . 2 |
12 | ralcom4 2734 | . . . . . 6 | |
13 | r19.23v 2566 | . . . . . . 7 | |
14 | 13 | albii 1450 | . . . . . 6 |
15 | 12, 14 | bitri 183 | . . . . 5 |
16 | nfv 1508 | . . . . . . . 8 | |
17 | ralrnmpo.2 | . . . . . . . 8 | |
18 | 16, 17 | ceqsalg 2740 | . . . . . . 7 |
19 | 18 | ralimi 2520 | . . . . . 6 |
20 | ralbi 2589 | . . . . . 6 | |
21 | 19, 20 | syl 14 | . . . . 5 |
22 | 15, 21 | bitr3id 193 | . . . 4 |
23 | 22 | ralimi 2520 | . . 3 |
24 | ralbi 2589 | . . 3 | |
25 | 23, 24 | syl 14 | . 2 |
26 | 11, 25 | syl5bb 191 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wb 104 wal 1333 wceq 1335 wcel 2128 cab 2143 wral 2435 wrex 2436 crn 4588 cmpo 5827 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-14 2131 ax-ext 2139 ax-sep 4083 ax-pow 4136 ax-pr 4170 |
This theorem depends on definitions: df-bi 116 df-3an 965 df-tru 1338 df-nf 1441 df-sb 1743 df-eu 2009 df-mo 2010 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-rex 2441 df-v 2714 df-un 3106 df-in 3108 df-ss 3115 df-pw 3545 df-sn 3566 df-pr 3567 df-op 3569 df-br 3967 df-opab 4027 df-cnv 4595 df-dm 4597 df-rn 4598 df-oprab 5829 df-mpo 5830 |
This theorem is referenced by: txcnp 12713 txcnmpt 12715 |
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